We show that for any subgroup ℋ of Out(FN), either ℋ contains an atoroidal element or a finite index subgroup ℋ' of ℋ fixes a nontrivial conjugacy class in FN. This result is an analog of Ivanov's subgroup theorem for mapping class groups and Handel–Mosher's subgroup theorem for Out(FN) in the setting of irreducible elements. This is joint work with Caglar Uyanik.